Question

question 13
lines fd and ge are parallel in the figure below.
what is the relationship between ∠dac and ∠eca?
a alternate interior angles
b alternate exterior angles
c same - side interior angles
d same - side exterior angles

Explanation:

Step1: Recall definitions

• Alternate interior angles: When two parallel lines are cut by a transversal, alternate interior angles are non - adjacent interior angles on opposite sides of the transversal.
• Alternate exterior angles: Non - adjacent exterior angles on opposite sides of the transversal when two parallel lines are cut by a transversal.
• Same - side interior angles: Interior angles on the same side of the transversal when two parallel lines are cut by a transversal.
• Same - side exterior angles: Exterior angles on the same side of the transversal when two parallel lines are cut by a transversal.

Step2: Analyze the position of \(\angle DAC\) and \(\angle ECA\)

Lines \(FD\) and \(GE\) are parallel. The line \(AC\) is a transversal. \(\angle DAC\) and \(\angle ECA\) are non - adjacent interior angles and are on opposite sides of the transversal \(AC\).

Answer:

A. Alternate interior angles